=Solution.=--The moment of the force _F_ exerted about the opposite end by the rear boy is _F_ × 8. The moment of the weight about the same point is 40 × (8 - 5) = 120. Therefore _F_ × 8 = 120, or _F_ = 15, the force exerted by the rear boy. The front boy exerts a force of _F_ whose moment about the other end of the rod is _F_ × 8. The moment of the weight about the same point is 40 × 5 = 200. Since the moment of _F_ equals this, 200 = _F_ × 8, or _F_ = 25. Hence the front boy exerts 25 lbs. and the rear boy 15 lbs. [Illustration: FIG. 68.--A couple.] =86. The Couple.=--If two equal parallel forces act upon a body along different lines in opposite directions, as in Fig. 68, they have no single resultant or there is no one force that will have the same effect as the two components acting together. A combination of forces of this kind is called a _couple_. Its tendency is to produce change of rotation in a body. An example is the action upon a compass needle which is rotated by a force which urges one end toward the north and by an equal force which urges the other end toward the south. Important Topics 1. Moment of force, how measured. 2. Parallel forces. 3. The two laws of parallel forces. 4. The couple. Exercises 1. Show by diagram how to arrange a three-horse evener so that each horse must take one-third of the load. 2. Two boys support a 10-ft. pole on their shoulders with a 40-lb. string of fish supported from it 4 ft. from the front boy. What load does each boy carry? Work by principle of moments. 3. If two horses draw a load exerting a combined pull of 300 lbs., what force must each exert if one is 28 in. and the other is 32 in. from the point of attachment of the evener to the load? [Illustration: FIG. 69.--Forces acting upon a stretched rope.] [Illustration: FIG. 70.--A crane with horizontal tie.] 4. A weight of 100 lbs. is suspended at the middle of a rope _ACB_ 20 ft. long. (See Fig. 69.) The ends of the rope are fastened at points _A_ and _B_ at the same height. Consider _D_ as the center of the line _AB_. What is the tension of the rope when _CD_ is 3 ft.? When _CD_ is 1 ft.? When _CD_ is 1 in.? 5. A crane is set up with the tie horizontal. (See Fig. 70.) If 1000 lbs. is to be lifted, find the tie stress and the boom stress if the boom angle is 30 degrees? If 45 degrees? 60 degrees? 6. A ball is placed on a plane inclined at an angle of 30 degrees to the horizontal. What fraction of its weight tends to cause motion down the plane? What effect does the other component of the weight have? Why? 7. A person weighing 150 lbs. is lying in a hammock. The distance between the supports is 15 ft. The hammock sags 4 ft. What is the tension in the supports at each end? What is the tension when the sag is only 1 ft.?